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We applied multiple parameters method (MPM) to obtain natural frequency of the nonlinear oscillator with rational restoring force. A frequency analysis is carried out and the relationship between the angular frequency and the initial amplitude is obtained in analytical/numerical form. This equation is analyzed in three cases: the relativistic harmonic oscillator, a mass attached of a stretched elastic wire and oscillations of a punctual charge in the electric field of charged ring. The three and four parameters solutions are obtained. The results obtained are compared with the numerical solution, showing good agreement.<o:p></o:p> </p

Oscillations of a Punctual Charge in the Electric Field of a Charged Ring: A Comparative Study